Question

the measures of the angles of a triangle are shown in the figure below. solve for x.
answer

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, if the angles of the triangle are \(74^{\circ}\), \(61^{\circ}\), and \(x^{\circ}\), then the equation is \(74 + 61+x=180\).

Step2: Simplify the left - hand side of the equation

First, add \(74\) and \(61\): \(74 + 61=135\). The equation becomes \(135+x = 180\).

Step3: Solve for \(x\)

Subtract \(135\) from both sides of the equation. Using the subtraction property of equality \(x=180 - 135\).

Answer:

\(x = 45\)